The Theoretical Investigation Of Atom Ionization In Intense Laser Field And Spontaneous Symmetry Breaking Of Bose-fermi Mixtures

The invention and application of the lasers have provided an advantageoustool to know the objective material world and opened many new fields. Intenselaser field-matter interactions and ultra-cold atoms are the two researchhotspots.Many novel phenomena can be found when atoms or molecules are exposed toan intense femtosecond laser pulse. Strong-field ionization, especiallynonsequential double ionization （NSDI） of atoms and molecules in intenselaser fields, is one of the important phenomena and has been thoroughlyinvestigated in recent years both theoretically and experimentally. This wasdiscovered experimentally to exhibit ion yields many orders of magnitudelarger than predicted by the single active electron approximation theory.A distinct “knee” signature in the double ionization yield plotted as afunction of intensity which is caused by the exceptionally strong electronpair correlation. Several mechanisms were proposed to explain the observedexperimental results. One of them is the rescattering model, i.e., the firstelectron which tunnels out from the atom is driven back by the laser ontoits parent ion at high velocity leading to the release of the second electronby means of inelastic scattering. Although we have known the mechanism ofNSDI, many questions remain unsettled regarding strong field doubleionization, and one that is completely open concerns polarization. The double ionization experiments have been done with linearly polarized light. But therescattering model predicts that the ion yield will lower under ellipticalor circular polarization than linearly polarized light because the returnelectron has less chance to encounter the atomic core, and this was quicklyaffirmed experimentally. So we need to study double ionization atoms ormolecules with circular or elliptical polarization light in theory.In order to describe intense laser field-matter interactions more reality,we use three-dimensional （3D） model. Nowadays, the computation is rathertime-consuming to solve the3D Schr dinger equation of two-electron atoms.However, classical approach has very big advantage and is ease to calculate.In this letter, we apply the classical ensemble method to study the ionizationof a3D model atom interacting with elliptically polarized light.Laser cooling and trap atoms are significant progresses of physics inrecently years. On this basis, there have been significant progresses inultra-cold atomic gas physics: Bose-Einstein condensates （BEC）, two bosonmixtures, Fermi degenerate atomic gases, and Bose-Fermi （BF） mixtures, andso on. In particular, the BF mixtures attract physical interests as a typicalexample where particles obeying different quantum statistics areintermingled. The study on the BF mixtures gives a big opportunity to obtaina lot of new knowledge on quantum many-body systems because we can constructmixtures with a variety of atomic-species combinations and the atomicinteractions in the mixtures can be controlled using the Feshbach-resonancemethod. Theoretical studies of the BF mixtures have been done on staticproperties, the phase structures and separation, collapse, the collectiveexcitations, and spontaneous symmetry breaking （SSB）.SSB is fundamental in disparate scenarios in physics ranging from cosmologyand particle physics to liquid crystals and superfluid helium. SSB is alsocrucial in BEC, where the U（1） symmetry is spontaneously broken. A simplebut reliable theoretical tool for the study of these trapped degenerate gasesis the density-functional theory. In particular, the Gross-Pitaevskiiequation （GPE）, which accurately describes BECs in dilute gases, is the Euler-Lagrange equation produced by the Thomas-Fermi （TF） density functionalwhich takes into account the inhomogeneity of the condensate. In BEC, boththe mean-field and the full quantum dynamics of SSB have been studied. Inparticular, in various two-dimensional （2D） settings, the matter-wavesolitons and the model of the BEC of dipolar atoms, which interact vialong-range forces. Theoretical studies of the SSB in BECs were extended intwo-component and three-component in double-well potential （DWP）, and alsostudied in BF mixture in one-dimensional （1D）. A straightforwardgeneralization may deal with the system including the confining potentialin both components, as well as a more general analysis of the TF approximation.A challenging possibility is to predict similar effects in multidimensionalBF mixtures.In the concrete, the main work in this thesis can be summarized as follows:1. We apply the classical ensemble method to study the ionization of a3Dmodel atom Kr or Xe interacting with an elliptically polarized laser pulsevarying with the value of the relative phase. We solve the Hamiltoniancanonical equations using the4th-order explicit symplectic algorithm obtainthe double ionization probabilities versus the increasing peak laserintensity varying with the value of the relative phase. We can see a remarkableknee structure for=0°and15°. This is the characteristic of the NSDI,which means that the electron-electron correlation is predominant at thesephases. Whereas with the increasing values of the relative phase the doubleionization probability drops rapidly, the knee structure disappears for=75°and90°. We can interpret these phenomena from the recollision modelas follows. The elliptically polarized laser field is linearly polarized for=0°. For the linearly polarized laser pulse, the outer electron is drivenalong the polarized axis, and thus has more chances to recollide with theother electron; while for the circularly polarized laser pulse, whichcontains a transverse component, the probability of recollisions is smaller.Similarly, when the value of the relative phase increases, the elliptically polarized laser field tends to be circularly polarized, the transversecomponent of the elliptically polarized laser field increases, therecollision probability reduces and hence the NSDI probability decreases.We also give the momentum spectra of electrons in the sequential ionizationregion under various relative phases. The high-momentum electrons areobtained when remarkable collision processes take place between the electronsand the nuclei in the inner of the ions. Finally, we investigate the correlatedmomenta of two-electron ionization of atoms.2. In this work, we introduce a physical model that gives rise to the SSBof the2D DWP in a BF system. SSB is a phenomenon in which symmetric statesin symmetric potentials appear to be broken when the strength of theself-attractive nonlinearity exceeds a certain critical value. Previously,this effect was studied in a1D setting. Our model is based on a2D set ofcoupled GP equations derived from the density functional in the unitaritylimit. We study the SSB in the trapped BF mixture with the DWP acting on bothspecies. We demonstrate that the SSB is possible by varying the values ofN_B and N_Fin the2D DWP for⁸⁷Rb and⁴⁰K atoms due to the attraction betweenthem. The3D phase diagrams of the asymmetry ratio of the bosons and thefermions in the （N_B,N_F）plane are calculated by means of numerical methods.They clearly show the transition from the symmetric ground state to theasymmetric one. Finally, we study the dynamical process of the SSB inducedby a gradual transformation of the single-well potential into the DWP. Thepopulations of the fermions and the bosons are mainly trapped in the samewell instead of equally distributed in the two wells with the increasedpotential barrier.